Free partition functions and an averaged holographic duality

Afkhami-Jeddi, Nima; Cohn, Henry; Hartman, Thomas; Tajdini, Amirhossein

doi:10.1007/jhep01(2021)130

Cited by 180 publications

(358 citation statements)

References 79 publications

(121 reference statements)

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“…For c ∈ (1, 4), the modular bootstrap bound for CFTs with chiral algebra A = U(1) c [23] or A = Vir [5] is at least as strong as…”

Section: Jhep02(2021)064mentioning

confidence: 99%

“…How are we to interpret this distinction in the context of 3d gravity? As we now argue, this has implications for ensemble averages over CFTs and their possible duality to theories of 3d gravity with asymptotically AdS boundary conditions [23,63,[107][108][109][110][111].…”

Section: Ensemble Averages and The Black Hole Thresholdmentioning

confidence: 99%

“…In unitary, compact CFTs, the degeneracies d h,h must satisfy the following three properties: The first of these, together with modularity, forms the backbone of the modular bootstrap program. Discreteness and integrality are sometimes observed as outputs of increasingly high-precision numerics in the modular bootstrap [5,8,10,23,24]. In addition, the existence of a normalizable vacuum state is sometimes assumed in both analytics and numerics.…”

Section: Introductionmentioning

confidence: 99%

“…To phrase this more rigorously, we define the following two spaces: 23 Z: the space of primary partition functions Z p (τ,τ ) of unitary, compact, irrational CFTs with a normalizable vacuum.…”

mentioning

confidence: 99%

“…. Pure higher-spin gravity also appears in connection with ensemble averaging over Narain moduli space[23,63].…”

mentioning

confidence: 99%

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Discreteness and integrality in Conformal Field Theory

Kaidi

Perlmutter

2021

J. High Energ. Phys.

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Various observables in compact CFTs are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but understanding of the abstract implications of discreteness and integrality for the space of CFTs is lacking. We systematically study these constraints in two-dimensional, non-holomorphic CFTs, making use of two main mathematical results. First, we prove a theorem constraining the behavior near the cusp of integral, vector-valued modular functions. Second, we explicitly construct non-factorizable, non-holomorphic cuspidal functions satisfying discreteness and integrality, and prove the non-existence of such functions once positivity is added. Application of these results yields several bootstrap-type bounds on OPE data of both rational and irrational CFTs, including some powerful bounds for theories with conformal manifolds, as well as insights into questions of spectral determinacy. We prove that in rational CFT, the spectrum of operator twists $$ t\ge \frac{c}{12} $$ t ≥ c 12 is uniquely determined by its complement. Likewise, we argue that in generic CFTs, the spectrum of operator dimensions $$ \Delta >\frac{c-1}{12} $$ Δ > c − 1 12 is uniquely determined by its complement, absent fine-tuning in a sense we articulate. Finally, we discuss implications for black hole physics and the (non-)uniqueness of a possible ensemble interpretation of AdS3 gravity.

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“…For c ∈ (1, 4), the modular bootstrap bound for CFTs with chiral algebra A = U(1) c [23] or A = Vir [5] is at least as strong as…”

Section: Jhep02(2021)064mentioning

confidence: 99%

Section: Ensemble Averages and The Black Hole Thresholdmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

“…. Pure higher-spin gravity also appears in connection with ensemble averaging over Narain moduli space[23,63].…”

mentioning

confidence: 99%

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Discreteness and integrality in Conformal Field Theory

Kaidi

Perlmutter

2021

J. High Energ. Phys.

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Holographic Duals of Symmetry Broken Phases

Antinucci,

Benini,

Rizi

2024

Fortschritte der Physik

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A novel interpretation of Symmetry Topological Field Theories (SymTFTs) as theories of gravity is explored by proposing a holographic duality where the bulk SymTFT (with the gauging of a suitable Lagrangian algebra) is dual to the universal effective field theory (EFT) that describes spontaneous symmetry breaking on the boundary. The authors tested this conjecture in various dimensions and with many examples involving different continuous symmetry structures, including non‐Abelian and non‐invertible symmetries, as well as higher groups. For instance, many Abelian SymTFTs are found to be dual to free theories of Goldstone bosons or generalized Maxwell fields, while non‐Abelian SymTFTs relate to non‐linear sigma models with target spaces defined by the symmetry groups. The analysis is also extended to include the non‐invertible axial symmetry, which is shown to be dual to axion‐Maxwell theory, and a non‐Abelian 2‐group structure in four dimensions, deriving a new parity‐violating interaction that has implications for the low‐energy dynamics of QCD.

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Entanglement island, miracle operators and the firewall

2022

J. High Energ. Phys.

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In this paper, we obtain some general results on information retrieval from the black hole interior, based on the recent progress on quantum extremal surface formula and entanglement island. We study an AdS black hole coupled to a bath with generic dynamics, and ask whether it is possible to retrieve information about a small perturbation in the interior from the bath system. We show that the one-norm distance between two reduced states in a bath region A is equal to the same quantity in the bulk quantum field theory for region AI where I is the entanglement island of A. This is a straightforward generalization of bulk-boundary correspondence in AdS/CFT. However, we show that a contradiction arises if we apply this result to a special situation when the bath dynamics includes a unitary operation that carries a particular measurement to a region A and send the result to another region W. Physically, the contradiction arises between transferability of classical information during the measurement, and non-transferability of quantum information which determines the entanglement island.We propose that the resolution of the contradiction is to realize that the state reconstruction formula does not apply to the special situation involving interior-information-retrieving measurements. This implies that the assumption of smooth replica AdS geometry with boundary condition set by the flat space bath has to break down when the particular measurement operator is applied to the bath. Using replica trick, we introduce an explicitly construction of such operator, which we name as “miracle operators”. From this construction we see that the smooth replica geometry assumption breaks down because we have to introduce extra replica wormholes connecting with the “simulated blackholes” introduced by the miracle operator. We study the implication of miracle operators in understanding the firewall paradox.

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Free partition functions and an averaged holographic duality

Cited by 180 publications

References 79 publications

Discreteness and integrality in Conformal Field Theory

Discreteness and integrality in Conformal Field Theory

Holographic Duals of Symmetry Broken Phases

Entanglement island, miracle operators and the firewall

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